This is difficult to explain, so bear with me. Construct will only recognize the tilemap from the first layout you run. The second layout will ignore the tiles in that instance of the tilemap and instead will use whatever tiles were present in the first instance of the tilemap before it was copied to the second layout. If the tilemap from the first layout was blank before it was copied to the second layout, you draw different tiles for each (ie neither layout is blank but the two instances of the tilemap are not the same), run the first layout and then go to the second layout, the tilemap will be blank.

Expected result:

The tiles drawn on each instance of a tilemap object should be saved for each instance. C2 should not expect there to be only one instance of each tilemap object.

The obvious workaround is to create a new tilemap object for every layout, but there are a number of reasons not to do this, the main one being added complexity. What if multiple layouts share the same event sheet and have events which reference the tilemap object? It would require you to duplicate events or create a family that acts as a container for all the tilemaps. What if you have many layouts using the same tilemap image, and have to edit the image? You would need to make the edit to every duplicate tilemap object. etc.

Browsers affected:

Chrome: yes

I have not tested on other browsers. If you think the browser is relevant then let me know.